This paper studies PD and PFI as statistical estimators of the ground truth DPG-PD and DGP-PFI, including bias and variance decompositions, and confidence interval estimators.
Whether the estimands themselves are desirable in specific data scenarios and model choices is out-of-scope for this work.
Others have done work in limitations of PFI and PD: For example [1]}, [2]}, [3]} show that interpretation methods produce misleading results under strongly dependent features (e.g. large correlation between features), [4]} assess whether PDs can be used to estimate causal effects, and [5]} studied whether PDs recover the linear relationship of the DGP when the relationship between target and features is linear.
Extrapolation when features are dependent might be one of the biggest issue for PD and PFI.
As one possible remedy, conditional variants of PDP and PFI [1]}, [7]}, [8]}, [9]} have been proposed.
For PD, the conditional variant is also called M-Plot [9]} and weights predictions according to how likely their respective feature values are for a given PD grid point.
Our proposed variance and confidence interval estimators and other results apply to both the original and conditional variants of PD and PFI, if not stated otherwise.
